A10340 | Three-dimensional Turtle Super Computer

A super computer has been built in the Turtle Academy of Sciences. The computer consists of $n·m·k$ CPUs. The architecture was the paralellepiped of size $n×m×k$ , split into $1×1×1$ cells, each cell contains exactly one CPU. Thus, each CPU can be simultaneously identified as a group of three numbers from the layer number from $1$ to $n$ , the line number from $1$ to $m$ and the column number from $1$ to $k$ .

In the process of the Super Computer's work the CPUs can send each other messages by the famous turtle scheme: CPU $(x,y,z)$ can send messages to CPUs $(x+1,y,z)$ , $(x,y+1,z)$ and $(x,y,z+1)$ (of course, if they exist), there is no feedback, that is, CPUs $(x+1,y,z)$ , $(x,y+1,z)$ and $(x,y,z+1)$ cannot send messages to CPU $(x,y,z)$ .

Over time some CPUs broke down and stopped working. Such CPUs cannot send messages, receive messages or serve as intermediates in transmitting messages. We will say that CPU $(a,b,c)$ controls CPU $(d,e,f)$ , if there is a chain of CPUs $(x_{i},y_{i},z_{i})$ , such that $(x_{1}=a,y_{1}=b,z_{1}=c)$ , $(x_{p}=d,y_{p}=e,z_{p}=f)$ (here and below $p$ is the length of the chain) and the CPU in the chain with number $i$ ( $i<p$ ) can send messages to CPU $i+1$ .

Turtles are quite concerned about the denial-proofness of the system of communication between the remaining CPUs. For that they want to know the number of critical CPUs. A CPU $(x,y,z)$ is critical, if turning it off will disrupt some control, that is, if there are two distinctive from $(x,y,z)$ CPUs: $(a,b,c)$ and $(d,e,f)$ , such that $(a,b,c)$ controls $(d,e,f)$ before $(x,y,z)$ is turned off and stopped controlling it after the turning off.

The first line contains three integers $n$ , $m$ and $k$ ( $1<=n,m,k<=100$ ) — the dimensions of the Super Computer.

Then $n$ blocks follow, describing the current state of the processes. The blocks correspond to the layers of the Super Computer in the order from $1$ to $n$ . Each block consists of $m$ lines, $k$ characters in each — the description of a layer in the format of an $m×k$ table. Thus, the state of the CPU $(x,y,z)$ is corresponded to the $z$ -th character of the $y$ -th line of the block number $x$ . Character "1" corresponds to a working CPU and character "0" corresponds to a malfunctioning one. The blocks are separated by exactly one empty line.

Print a single integer — the number of critical CPUs, that is, such that turning only this CPU off will disrupt some control.